I would like to graphically represent the R-squared values of the linear regression models I have created, however, I have a mixture of both linear (LM) and generalized least square (GLS) models. The output of the former produces an adjusted R-squared value, whereas, the latter does not. Therefore, for the GLS models, I have calculated pseudo R-squared values using the nagelkerke function in R. This function produces 3 pseudo R-squared values, namely:
1. McFadden,
2. Cox and Snell (ML), and
3. Nagelkerke (Cragg and Uhler).
Each value is quite different from the others, and I am not sure as to which value is the correct one to use, specifically in the context of a GLS model. Furthermore, once I have selected an adequate pseudo R-squared value, will it be comparable to the adjusted R-squared values produced by the LM model output?
Cox and Snell’s R2Cs is based on the deviance of the model (-2LL(new)) and the deviance of the baseline model (-2LL(baseline)), and the sample size, n.
R2Cs=1-exp((-2LL(new)-(-2LL(baseline))/n
However, this statistic never reaches its theoretical maximum of 1. Therefore, Nagelkerke (1991) suggested the following amendment (Nagelkerke’s RN2):
R2N = R2Cs/(1-exp(-(-2LL(baseline))/n)
Although all of these measures differ in their computation (and the answers you get), conceptually they are somewhat similar. So, in terms of interpretation they can be seen as similar to the R2 in linear regression in that they provide a gauge of the substantive significance of the model.
In general no they are not comparable even though all of them claim to be goodness of fit statistics. Google each one to see what if anything can be said about the aggregate. Best, David Booth
I would add to your list Efron's pseudo r-squared. Efron's pseudo r-squared, and I think Cox and Snell, equal r-squared if the model under consideration is an OLS model. So, if you are trying to use a measure that is applicable across those different model types, those might be useful.
Dear Baker,
For many types of models, R-squared is not defined. These include relatively common models like logistic regression. For these models, pseudo R-squared measures can be calculated. A pseudo R-squared is not directly comparable to the R-squared for OLS models. Nor can it can be interpreted as the proportion of the variability in the dependent variable that is explained by model. Instead, pseudo R-squared measures are relative measures among similar models indicating how well the model explains the data. See R Handbook: p-values and R-square Values for Models.
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